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Cotygodniowe seminarium badawcze
2020-01-15, godz. 16:15, 5050
Michael Levin (Ben-Gurion University of the Negev, Israel)
Based on a result of H. Torunczyk, R. Pol showed that a light map f: X->Y from a compactum X with dim X > 2 to a finite dimensional compactum Y is injective on a non-trivial subcontinuum of X. Pol also showed that in the above statement the restriction dim X > 2 is necessary a...
2020-01-08, godz. 16:15, 5050
Witold Marciszewski (University of Warsaw)
Countable dense homogeneous linear topological spaces
Recall that a topological space X is countable dense homogeneous (CDH) if X is separable, and given countable dense subsets D,E of X, there is an autohomeomorphism of X mapping D onto E. This is a classical notion tracing back to works of Cantor, Frechet and Brouwer. The canonical examples of CDH sp...
2019-12-18, godz. 16:15, 5050
Damian Sobota (Kurt Gödel Research Center, University of Vienna)
Convergence of measures in the random model
A Boolean algebra B has the Vitali--Hahn--Saks property if every sequence of measures on B which converges to 0 on elements of B converges also to 0 on every Borel subset of the Stone space of B. Examples of Boolean algebras having the property include e.g. sigma-complete ones. Some time ago we show...
2019-12-11, godz. 16:15, 5050
Piotr Szewczak (Cardinal Wyszyński University in Warsaw)
Null-additive sets and the property gamma
A subset X of the real line is null-additive if for each null set Y, the set X+Y is null. Under Martin Axiom, Galvin nad Miller constructed an uncountable null-additive set whose continuous images are also null-additive; this set has the property gamma, a strong combinatorial covering property. Bart...
2019-12-04, godz. 16:15, 5050
Szymon Głąb (Institute of Mathematics Technical University of Łódź)
Inverse limits of finite graphs (joint project with Stefan Geschke and Wiesław Kubiś)
The random graph R is the unique countable graph which contains isomorphic copies of all countable graphs and is homogeneous in the sense that every isomorphism between its finite subgraphs extends to an automorphism of R. Actually, the existence, universality and uniqueness of the random graph foll...
2019-11-27, godz. 16:15, 5050
Grzegorz Plebanek (University of Wrocław)
For a compact space K, we consider the space P(K) of regular probability measures on K, equipped with the weak* topology. For zerodimensional spaces K, we can, equvalently, speak of P(A), the space of finitely additive measures on a Boolean algebra A (with the topology of converence on element...
2019-11-06, godz. 16:15, 5050
Piotr Zakrzewski (University of Warsaw)
On Mazurkiewicz's sets and regularity properties of sigma-ideals
The talk will present results from a joint paper with Roman Pol. Let f:X --> Y be a continuous surjection of the compact metrizable space X onto an uncountable compact metrizable space Y. A Mazurkiewicz set for f is a G_{delta sigma}-set M in X which is a partial selector for f and each G_de...
2019-10-31, godz. 16:15, 5050
Arturo Antonio Martínez Celis Rodríguez (IMPAN)
Cardinal Invariants and Rosenthal families
Rosenthal's lemma is a classical result that concerns sequences of measures on pairwise disjoint sets and a Rosenthal family is a collection of infinite subsets of the natural numbers that can replace the collection of all infinite subsets of natural numbers in Rosenthal's lemma. In this talk we wil...
2019-10-23, godz. 16:15, 5050
Roman Pol (University of Warsaw)
On uniformly tight sets of probability measures on the rationals
The talk will present results obtained jointly with Piotr Zakrzewski. Let P(Q) be the space of probability measures on the rationals Q, equipped with the weak topology. A set A in P(Q) is uniformly tight if for any r > 0 there is a compact set C in Q such that u(C) > 1 - r for ever...
2019-10-16, godz. 16:15, 5050
Mikołaj Krupski (University of Warsaw)
Hereditarily Baire hyperspaces, filters and spaces of measures - part 2
This part does not depend on the material presented under the same title during the first part of the talk. A topological space X is Baire if the intersection of a countable family of open dense sets in X is dense. We say that X is hereditarily Baire if every closed subspace of X is Baire. It wa...
